The 37-year-old had teed off on Sunday two strokes off the pace, hoping to become the first Swedish male to win one of golf's major championships.
But, despite a level par round of 70, he ended up three shots behind American winner Jason Dufner who closed with a 68.
Stenson offset an eagle and two birdies by posting four bogeys as he covered the final five holes in two over par to finish as the leading European.
The Ryder Cup player is now back up to No 10 in the World Ranking thanks to a very good 12 months, having slipped to 230th at the start of 2012.
More recently he has gone 3rd-2nd-2nd-3rd in his last four starts that included a runner-up slot in The Open Championship at Muirfield.
He said: "I'm happy and proud of my performance. Didn't play my absolute best today, that's for sure but I was still giving it a good fight.
"I had an unbelievable round and some great tournaments in the last month.
"I will take a lot of positives out of that, got a lot of big tournaments left this year. Really excited, going to work hard on my game."
Stenson's final round partner was compatriot Jonas Blixt who finished fourth - one stroke further back.
Blixt added: "Coming down the stretch, got a little jittery but it's kind of exciting to be up there with those guys and seeing your name.
"I've got to get used to that a little more for next time.
"You get jittery. You get very excited and it's a lot of fun to contend. But this is a new stage. I'll probably handle it a little better next time.
"I played well. I learned a lot, especially about myself and how I would react in a situation like this.
"I'm going to go back and analyse it a little more and see if I can do better next time. It was a learning experience and a lot of fun."